Subgroups — C₂×C₃×#65928 #14495255

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4099	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#4083	C₂	1	3	yes	maximal, complemented
4	C₂×C₃×#4082	C₂	1	3	yes	maximal, complemented
5	C₃×#65928	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃×#4031	C₂	1	6	yes	maximal, complemented
7	C₂×#65928	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic, complemented
9	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic, complemented
10	C₂²×C₃×C₅×D₄	C₂²	1	3	yes	—
11	C₂²×C₃×C₂²⋊D₅	C₂²	1	6	yes	—
12	C₂²×C₃×Dic₁₀	C₂²	1	3	yes	complemented
13	C₃×C₅×#120	C₂²	1	8	yes	complemented
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	complemented
15	C₃×#4099	C₂²	1	16	yes	complemented
16	C₂×C₃×C₂²⋊Dic₅	C₂²	1	3	yes	complemented
17	C₂×C₃×C₂²⋊Dic₅	C₂²	1	6	yes	complemented
18	C₃×#4083	C₂²	1	24	yes	complemented
19	C₃×#4082	C₂²	1	24	yes	complemented
20	C₂×C₃×#685	C₂²	1	6	yes	complemented
21	C₂×C₃×C₄×Dic₅	C₂²	1	3	yes	complemented
22	C₃×#4031	C₂²	1	48	yes	complemented
23	C₂×C₃×H(3,𝔽₄)	—	5	1	no	maximal, Hall
24	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×#4099	C₂×C₃	1	2	yes	complemented
26	C₂×#4083	C₂×C₃	1	3	yes	complemented
27	C₂×#4082	C₂×C₃	1	3	yes	complemented
28	#65928	C₂×C₃	1	16	yes	direct product factor
29	C₂×#4031	C₂×C₃	1	6	yes	complemented
30	C₂⁴×C₃×C₅	—	4	6	no	—
31	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
32	C₂⁴×C₃×C₅	C₂³	1	3	yes	—
33	C₂⁴×C₃×C₅	C₂³	1	4	yes	complemented
34	C₂³×C₃×D₅	—	4	6	no	—
35	C₂³×C₃×D₅	C₂³	1	2	yes	—
36	C₂³×C₃×D₅	C₂³	1	4	yes	complemented
37	C₂×C₃×C₅×D₄	—	4	6	no	—
38	C₂×C₃×C₅×D₄	C₂³	1	12	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
40	C₂×C₃×C₂²⋊D₅	—	4	12	no	—
41	C₂×C₃×C₂²⋊D₅	C₂³	1	24	yes	—
42	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
43	C₂×C₃×Dic₁₀	—	4	6	no	—
44	C₂×C₃×Dic₁₀	C₂³	1	12	yes	complemented
45	C₃×C₅×C₂²⋊C₄	C₂³	1	12	yes	complemented
46	C₃×C₂²⋊Dic₅	C₂³	1	12	yes	complemented
47	C₃×C₂²⋊Dic₅	C₂³	1	24	yes	complemented
48	C₃×#685	C₂³	1	24	yes	complemented
49	C₃×C₄×Dic₅	C₂³	1	12	yes	complemented
50	C₃×H(3,𝔽₄)	—	5	16	no	—
51	C₂×C₃×#124	—	5	3	no	—
52	C₂×C₃×#124	—	5	6	no	—
53	C₂×C₃×#120	—	5	3	no	—
54	C₂×C₃×#120	—	5	2	no	—
55	C₂×C₃×#120	D₅	1	1	yes	characteristic, complemented
56	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
57	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
58	C₂²×C₅×D₄	C₂²×C₃	1	3	yes	—
59	C₂²×C₂²⋊D₅	C₂²×C₃	1	6	yes	—
60	C₂²×Dic₁₀	C₂²×C₃	1	3	yes	complemented
61	C₅×#120	C₂²×C₃	1	8	yes	complemented
62	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	complemented
63	#4099	C₂²×C₃	1	16	yes	complemented
64	C₂×C₂²⋊Dic₅	C₂²×C₃	1	6	yes	complemented
65	C₂×C₂²⋊Dic₅	C₂²×C₃	1	3	yes	complemented
66	#4083	C₂²×C₃	1	24	yes	complemented
67	#4082	C₂²×C₃	1	24	yes	complemented
68	C₂×#685	C₂²×C₃	1	6	yes	complemented
69	C₂×C₄×Dic₅	C₂²×C₃	1	3	yes	complemented
70	#4031	C₂²×C₃	1	48	yes	complemented
71	C₂×H(3,𝔽₄)	—	5	1	no	Sylow
72	C₂³×C₃×C₅	—	2	12	no	—
73	C₂³×C₃×C₅	—	2	6	no	—
74	C₂³×C₃×C₅	—	2	6	no	—
75	C₂³×C₃×C₅	—	4	12	no	—
76	C₂³×C₃×C₅	—	4	16	no	—
77	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
78	C₂³×C₃×C₅	C₂⁴	1	6	yes	—
79	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
80	C₂²×C₃×D₅	—	2	12	no	—
81	C₂²×C₃×D₅	—	4	12	no	—
82	C₂²×C₃×D₅	—	4	16	no	—
83	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
84	C₃×C₅×D₄	—	4	12	no	—
85	C₂×C₃×C₄×C₅	—	2	6	no	—
86	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
87	C₃×C₂²⋊D₅	—	4	24	no	—
88	C₂×C₃×Dic₅	—	2	12	no	—
89	C₂×C₃×Dic₅	C₂⁴	1	12	yes	—
90	C₃×Dic₁₀	—	4	12	no	—
91	C₂⁵×C₃	—	5	1	no	—
92	C₂⁵×C₃	C₂×D₅	1	1	yes	characteristic, complemented
93	C₂²×C₃×Q₈	—	5	3	no	—
94	C₂²×C₃×D₄	—	5	6	no	—
95	C₂²×C₃×D₄	C₂×D₅	1	3	yes	—
96	C₃×#124	—	5	24	no	—
97	C₃×#124	—	5	48	no	—
98	C₃×#120	—	5	16	no	—
99	C₃×#120	—	5	24	no	—
100	C₃×#120	C₂×D₅	1	8	yes	complemented
101	C₂×C₃×C₂²⋊C₄	—	5	3	no	—
102	C₂×C₃×C₂²⋊C₄	—	5	6	no	—
103	C₂×C₃×C₂²⋊C₄	—	5	6	no	—
104	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	3	yes	complemented
105	C₂×C₃×C₄²	—	5	3	no	—
106	C₂⁴×C₅	—	4	6	no	—
107	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
108	C₂⁴×C₅	C₂³×C₃	1	3	yes	—
109	C₂⁴×C₅	C₂³×C₃	1	4	yes	complemented
110	C₂³×D₅	—	4	6	no	—
111	C₂³×D₅	C₂³×C₃	1	2	yes	—
112	C₂³×D₅	C₂³×C₃	1	4	yes	complemented
113	C₂×C₅×D₄	—	4	6	no	—
114	C₂×C₅×D₄	C₂³×C₃	1	12	yes	—
115	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
116	C₂×C₂²⋊D₅	—	4	12	no	—
117	C₂×C₂²⋊D₅	C₂³×C₃	1	24	yes	—
118	C₂²×Dic₅	C₂³×C₃	1	6	yes	—
119	C₂×Dic₁₀	—	4	6	no	—
120	C₂×Dic₁₀	C₂³×C₃	1	12	yes	complemented
121	C₅×C₂²⋊C₄	C₂³×C₃	1	12	yes	complemented
122	C₂²⋊Dic₅	C₂³×C₃	1	24	yes	complemented
123	C₂²⋊Dic₅	C₂³×C₃	1	12	yes	complemented
124	#685	C₂³×C₃	1	24	yes	complemented
125	C₄×Dic₅	C₂³×C₃	1	12	yes	complemented
126	H(3,𝔽₄)	—	5	16	no	—
127	C₂×#124	—	5	3	no	—
128	C₂×#124	—	5	6	no	—
129	C₂×#120	—	5	2	no	—
130	C₂×#120	—	5	3	no	—
131	C₂×#120	C₃×D₅	1	1	yes	characteristic, complemented
132	C₂²×C₃×C₅	—	2	12	no	—
133	C₂²×C₃×C₅	—	2	6	no	—
134	C₂²×C₃×C₅	—	2	6	no	—
135	C₂²×C₃×C₅	—	4	16	no	—
136	C₂²×C₃×C₅	—	4	4	no	—
137	C₂²×C₃×C₅	—	4	12	no	—
138	C₂²×C₃×C₅	H(5,𝔽₂)	1	6	yes	—
139	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
140	C₂×C₃×D₅	—	2	12	no	—
141	C₂×C₃×D₅	—	4	16	no	—
142	C₂×C₃×D₅	—	4	8	no	—
143	C₃×C₄×C₅	—	2	6	no	—
144	C₃×Dic₅	—	2	12	no	—
145	C₂⁴×C₃	—	4	6	no	—
146	C₂⁴×C₃	—	5	2	no	—
147	C₂⁴×C₃	—	5	4	no	—
148	C₂⁴×C₃	—	20	6	no	—
149	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
150	C₂⁴×C₃	C₂²×D₅	1	3	yes	—
151	C₂⁴×C₃	C₂²×D₅	1	4	yes	complemented
152	C₂×C₃×Q₈	—	5	12	no	—
153	C₂×C₃×Q₈	—	20	6	no	—
154	C₂×C₃×D₄	—	4	6	no	—
155	C₂×C₃×D₄	—	5	24	no	—
156	C₂×C₃×D₄	—	20	12	no	—
157	C₂×C₃×D₄	C₂²×D₅	1	12	yes	—
158	C₂²×C₃×C₄	—	5	6	no	—
159	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
160	C₃×C₂²⋊C₄	—	5	12	no	—
161	C₃×C₂²⋊C₄	—	5	24	no	—
162	C₃×C₂²⋊C₄	—	5	24	no	—
163	C₃×C₂²⋊C₄	C₂²×D₅	1	12	yes	complemented
164	C₃×C₄²	—	5	12	no	—
165	C₂³×C₅	—	2	12	no	—
166	C₂³×C₅	—	2	6	no	—
167	C₂³×C₅	—	2	6	no	—
168	C₂³×C₅	—	4	12	no	—
169	C₂³×C₅	—	4	16	no	—
170	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
171	C₂³×C₅	C₂⁴×C₃	1	6	yes	—
172	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
173	C₂²×D₅	—	2	12	no	—
174	C₂²×D₅	—	4	12	no	—
175	C₂²×D₅	—	4	16	no	—
176	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
177	C₅×D₄	—	4	12	no	—
178	C₂×C₄×C₅	—	2	6	no	—
179	C₂×C₄×C₅	C₂⁴×C₃	1	6	yes	—
180	C₂²⋊D₅	—	4	24	no	—
181	C₂×Dic₅	—	2	12	no	—
182	C₂×Dic₅	C₂⁴×C₃	1	12	yes	—
183	Dic₁₀	—	4	12	no	—
184	C₂⁵	—	5	1	no	—
185	C₂⁵	C₂×C₃×D₅	1	1	yes	characteristic, complemented
186	C₂²×Q₈	—	5	3	no	—
187	C₂²×D₄	—	5	6	no	—
188	C₂²×D₄	C₂×C₃×D₅	1	3	yes	—
189	#124	—	5	24	no	—
190	#124	—	5	48	no	—
191	#120	—	5	16	no	—
192	#120	—	5	24	no	—
193	#120	C₂×C₃×D₅	1	8	yes	complemented
194	C₂×C₂²⋊C₄	—	5	3	no	—
195	C₂×C₂²⋊C₄	—	5	6	no	—
196	C₂×C₂²⋊C₄	—	5	6	no	—
197	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	3	yes	complemented
198	C₂×C₄²	—	5	3	no	—
199	C₂×C₃×C₅	—	4	2	no	—
200	C₂×C₃×C₅	—	4	6	no	—
201	C₂×C₃×C₅	H(3,𝔽₄)	1	4	yes	complemented
202	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	3	yes	—
203	C₃×D₅	—	4	4	no	—
204	C₂³×C₃	—	2	6	no	—
205	C₂³×C₃	—	2	6	no	—
206	C₂³×C₃	—	2	12	no	—
207	C₂³×C₃	—	4	12	no	—
208	C₂³×C₃	—	4	16	no	—
209	C₂³×C₃	—	5	4	no	—
210	C₂³×C₃	—	10	12	no	—
211	C₂³×C₃	—	20	12	no	—
212	C₂³×C₃	—	20	16	no	—
213	C₂³×C₃	C₂³×D₅	1	2	yes	—
214	C₂³×C₃	C₂³×D₅	1	6	yes	—
215	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
216	C₃×Q₈	—	20	12	no	—
217	C₃×D₄	—	4	12	no	—
218	C₃×D₄	—	20	24	no	—
219	C₂×C₃×C₄	—	2	6	no	—
220	C₂×C₃×C₄	—	5	12	no	—
221	C₂×C₃×C₄	—	10	12	no	—
222	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
223	C₂²×C₅	—	2	12	no	—
224	C₂²×C₅	—	2	6	no	—
225	C₂²×C₅	—	2	6	no	—
226	C₂²×C₅	—	4	16	no	—
227	C₂²×C₅	—	4	4	no	—
228	C₂²×C₅	—	4	12	no	—
229	C₂²×C₅	C₃×H(5,𝔽₂)	1	6	yes	—
230	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
231	C₂×D₅	—	2	12	no	—
232	C₂×D₅	—	4	16	no	—
233	C₂×D₅	—	4	8	no	—
234	C₄×C₅	—	2	6	no	—
235	Dic₅	—	2	12	no	—
236	C₂⁴	—	4	6	no	—
237	C₂⁴	—	5	2	no	—
238	C₂⁴	—	5	4	no	—
239	C₂⁴	—	20	6	no	—
240	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
241	C₂⁴	C₂²×C₃×D₅	1	3	yes	—
242	C₂⁴	C₂²×C₃×D₅	1	4	yes	complemented
243	C₂×Q₈	—	5	12	no	—
244	C₂×Q₈	—	20	6	no	—
245	C₂×D₄	—	4	6	no	—
246	C₂×D₄	—	5	24	no	—
247	C₂×D₄	—	20	12	no	—
248	C₂×D₄	C₂²×C₃×D₅	1	12	yes	—
249	C₂²×C₄	—	5	6	no	—
250	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
251	C₂²⋊C₄	—	5	12	no	—
252	C₂²⋊C₄	—	5	24	no	—
253	C₂²⋊C₄	—	5	24	no	—
254	C₂²⋊C₄	C₂²×C₃×D₅	1	12	yes	complemented
255	C₄²	—	5	12	no	—
256	C₃×C₅	C₂×H(3,𝔽₄)	1	1	yes	characteristic, complemented, Hall
257	C₂²×C₃	—	2	6	no	—
258	C₂²×C₃	—	2	6	no	—
259	C₂²×C₃	—	2	12	no	—
260	C₂²×C₃	—	4	16	no	—
261	C₂²×C₃	—	4	12	no	—
262	C₂²×C₃	—	4	4	no	—
263	C₂²×C₃	—	10	12	no	—
264	C₂²×C₃	—	20	16	no	—
265	C₂²×C₃	—	20	8	no	—
266	C₂²×C₃	#4144	1	6	yes	—
267	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
268	C₃×C₄	—	2	6	no	—
269	C₃×C₄	—	10	12	no	—
270	C₂×C₅	—	4	2	no	—
271	C₂×C₅	—	4	6	no	—
272	C₂×C₅	C₃×H(3,𝔽₄)	1	4	yes	complemented
273	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	3	yes	—
274	D₅	—	4	4	no	—
275	C₂³	—	2	6	no	—
276	C₂³	—	2	6	no	—
277	C₂³	—	2	12	no	—
278	C₂³	—	4	12	no	—
279	C₂³	—	4	16	no	—
280	C₂³	—	5	4	no	—
281	C₂³	—	10	12	no	—
282	C₂³	—	20	12	no	—
283	C₂³	—	20	16	no	—
284	C₂³	C₂³×C₃×D₅	1	2	yes	—
285	C₂³	C₂³×C₃×D₅	1	6	yes	—
286	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
287	Q₈	—	20	12	no	—
288	D₄	—	4	12	no	—
289	D₄	—	20	24	no	—
290	C₂×C₄	—	2	6	no	—
291	C₂×C₄	—	5	12	no	—
292	C₂×C₄	—	10	12	no	—
293	C₂×C₄	C₂³×C₃×D₅	1	6	yes	—
294	C₂×C₃	—	4	6	no	—
295	C₂×C₃	—	4	2	no	—
296	C₂×C₃	—	20	4	no	—
297	C₂×C₃	#65928	1	4	yes	direct product factor
298	C₂×C₃	C₂×#4144	1	3	yes	—
299	C₅	C₂×C₃×H(3,𝔽₄)	1	1	yes	characteristic, complemented, Sylow
300	C₂²	—	2	6	no	—
301	C₂²	—	2	6	no	—
302	C₂²	—	2	12	no	—
303	C₂²	—	4	16	no	—
304	C₂²	—	4	12	no	—
305	C₂²	—	4	4	no	—
306	C₂²	—	10	12	no	—
307	C₂²	—	20	16	no	—
308	C₂²	—	20	8	no	—
309	C₂²	C₃×#4144	1	6	yes	—
310	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
311	C₄	—	2	6	no	—
312	C₄	—	10	12	no	—
313	C₃	C₂×#65928	1	1	yes	characteristic, direct product factor, Sylow
314	C₂	—	4	6	no	—
315	C₂	—	4	2	no	—
316	C₂	—	20	4	no	—
317	C₂	C₃×#65928	1	4	yes	direct product factor
318	C₂	C₂×C₃×#4144	1	3	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#120	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#120	D₅
hypocenter	C₅	C₂×C₃×H(3,𝔽₄)
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#120

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×C₅×#120	C₂	semidirect
2. C₂×C₃×#4099	C₂	semidirect
3. C₂×C₃×#4083	C₂	semidirect
4. C₂×C₃×#4082	C₂	semidirect
5. C₃×#65928	C₂	direct (N × H)
6. C₂×C₃×#4031	C₂	semidirect
7. C₂×#65928	C₃	direct (N × H)
8. C₂⁵×C₃×C₅	C₂²	semidirect
9. C₂⁴×C₃×D₅	C₂²	semidirect
12. C₂²×C₃×Dic₁₀	C₂²	semidirect
13. C₃×C₅×#120	C₂²	semidirect
14. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
15. C₃×#4099	C₂²	semidirect
16. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
17. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
18. C₃×#4083	C₂²	semidirect
19. C₃×#4082	C₂²	semidirect
20. C₂×C₃×#685	C₂²	semidirect
21. C₂×C₃×C₄×Dic₅	C₂²	semidirect
22. C₃×#4031	C₂²	semidirect
24. C₂×C₅×#120	C₂×C₃	semidirect
25. C₂×#4099	C₂×C₃	semidirect
26. C₂×#4083	C₂×C₃	semidirect
27. C₂×#4082	C₂×C₃	semidirect
28. #65928	C₂×C₃	direct (N × H)
29. C₂×#4031	C₂×C₃	semidirect
33. C₂⁴×C₃×C₅	C₂³	semidirect
36. C₂³×C₃×D₅	C₂³	semidirect
44. C₂×C₃×Dic₁₀	C₂³	semidirect
45. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
46. C₃×C₂²⋊Dic₅	C₂³	semidirect
47. C₃×C₂²⋊Dic₅	C₂³	semidirect
48. C₃×#685	C₂³	semidirect
49. C₃×C₄×Dic₅	C₂³	semidirect
55. C₂×C₃×#120	D₅	semidirect
56. C₂⁵×C₅	C₂²×C₃	semidirect
57. C₂⁴×D₅	C₂²×C₃	semidirect
60. C₂²×Dic₁₀	C₂²×C₃	semidirect
61. C₅×#120	C₂²×C₃	semidirect
62. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
63. #4099	C₂²×C₃	semidirect
64. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
65. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
66. #4083	C₂²×C₃	semidirect
67. #4082	C₂²×C₃	semidirect
68. C₂×#685	C₂²×C₃	semidirect
69. C₂×C₄×Dic₅	C₂²×C₃	semidirect
70. #4031	C₂²×C₃	semidirect
92. C₂⁵×C₃	C₂×D₅	semidirect
100. C₃×#120	C₂×D₅	semidirect
104. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
109. C₂⁴×C₅	C₂³×C₃	semidirect
112. C₂³×D₅	C₂³×C₃	semidirect
120. C₂×Dic₁₀	C₂³×C₃	semidirect
121. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
122. C₂²⋊Dic₅	C₂³×C₃	semidirect
123. C₂²⋊Dic₅	C₂³×C₃	semidirect
124. #685	C₂³×C₃	semidirect
125. C₄×Dic₅	C₂³×C₃	semidirect
131. C₂×#120	C₃×D₅	semidirect
151. C₂⁴×C₃	C₂²×D₅	semidirect
163. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
185. C₂⁵	C₂×C₃×D₅	semidirect
193. #120	C₂×C₃×D₅	semidirect
197. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
201. C₂×C₃×C₅	H(3,𝔽₄)	semidirect
242. C₂⁴	C₂²×C₃×D₅	semidirect
254. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
256. C₃×C₅	C₂×H(3,𝔽₄)	semidirect
272. C₂×C₅	C₃×H(3,𝔽₄)	semidirect
297. C₂×C₃	#65928	direct (N × H)
299. C₅	C₂×C₃×H(3,𝔽₄)	semidirect
313. C₃	C₂×#65928	direct (N × H)
317. C₂	C₃×#65928	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×#120	2
C₂×C₃×#4099	2
C₂×C₃×#4083	2
C₂×C₃×#4082	2
C₃×#65928	2
C₂×C₃×#4031	2
C₂×#65928	3
C₂×C₃×H(3,𝔽₄)	5

Subgroups — C2×C3×#65928 #14495255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65928 #14495255